apl: life Conway via 9-shift toroidal sum (+7 tests, 287/287)

lib/apl/tests/programs/life.apl

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+⍝ Conway's Game of Life — toroidal one-liner
+⍝
+⍝ The classic Roger Hui formulation:
+⍝   life ← {⊃1 ⍵ ∨.∧ 3 4 = +/ +/ ¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵}
+⍝
+⍝ Read right-to-left:
+⍝   ⊂⍵                : enclose the board (so it's a single scalar item)
+⍝   ¯1 0 1 ⌽¨ ⊂⍵      : produce 3 horizontally-shifted copies
+⍝   ¯1 0 1 ∘.⊖ …      : outer-product with vertical shifts → 3×3 = 9 shifts
+⍝   +/ +/ …           : sum the 9 boards element-wise → neighbor-count + self
+⍝   3 4 = …           : boolean — count is exactly 3 or exactly 4
+⍝   1 ⍵ ∨.∧ …         : "alive next" iff (count=3) or (alive AND count=4)
+⍝   ⊃ …               : disclose back to a 2D board
+⍝
+⍝ Rules in plain language:
+⍝   - dead cell + 3 live neighbors → born
+⍝   - live cell + 2 or 3 live neighbors → survives
+⍝   - all else → dies
+⍝
+⍝ Toroidal: edges wrap (rotate is cyclic).
+
+life ← {⊃1 ⍵ ∨.∧ 3 4 = +/ +/ ¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵}